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**Ques 1: Which of the following expressions are polynomials in one variable and which are not? ****State reasons for your answer. (i) 4x ^{2} – 3x + 7 (ii) y^{2} + 2 (iii) **

**Ans:** (i) 4x^{2} – 3x + 7

⇒ 4x^{2} – 3x + 7x^{0}

∵ All the exponents of x are whole numbers.

∴ 4x^{2} – 3x + 7 is a polynomial in one variable.

∵ All the exponents of y are whole numbers.

∴ y^{2} + is a polynomial in one variable.

∵ 1/2 is not a whole number,

∴ 3t^{1/2} + is not a polynomial.

ﬁ y + 2 ◊ y–1

∵ (–1) is not a whole number.

∴ is not a polynomial.

(v) x^{10} + y^{3} + t^{50}

∵ Exponent of every variable is a whole number,

∴ x^{10 }+ y^{3} + t^{50} is a polynomial in x, y and t, i.e. in three variables.

**Ques 2: Write the co-efficients of x ^{2} in each of the following: **

**(i) 2 + x ^{2} + x (ii) 2 – x^{2} + x^{3} (iii) **

**(iv) ****Ans:** (i) 2 + x^{2} + x The co-efficient of x^{2} is 1.

(ii)** **2 – x^{2} + x^{3} The co-efficient of x^{2 }is (–1).

(iii)

∴ The co-efficient of x^{2} is 0.

**Ques 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100. ****Ans:** (i) A binomial of degree 35 can be: 3x^{35} – 4

(ii) A monomial of degree 100 can be: ^{ }

**Ques 4: Write the degree of each of the following polynomials: (i) 5x ^{3} + 4x^{2} + 7x (ii) 4 – y^{2} (iii) **

**Ans: **(i) 5x^{3} + 4x^{2} + 7x

∵ The highest exponent of x is 3.

∴ The degree of the polynomial is 3.

(ii) 4 – y^{2}

∵ The highest exponent of y is 2.

∴ The degree of the polynomial is 2.

(iii)

∵ The highest exponent of t is 1.

∴ The degree of the polynomial is 1.

( iv) 3 since, 3 = 3x^{0} [∵ x^{0} = 1]

∴ The degree of the polynomial 3 is 0.

**Ques 5: Classify the following as linear, quadratic and cubic polynomials: **

**(i) x ^{2 }+ x (ii) x – x^{3} (iii) y + y^{2} + 4 (iv) 1 + x ( v ) 3t (vi) r^{2 }(vii) 7x^{3}**

Ans:

(i) x^{2} + x ∵ The degree of x^{2} + x is 2.

∴ It is a quadratic polynomial.

(ii) x – x^{3}

∵ The degree of x – x^{3} is 3.

∴ It is a cubic polynomial.

(iii) y + y^{2 }+ 4

∵ The degree of y + y^{2} + 4 is 2.

∴ It is a quadratic polynomial.

(iv) 1 + x

∵ The degree of 1 + x is 1.

∴ It is a linear polynomial.

(v) 3t

∵ The degree of 3t is 1.

∴ It is a linear polynomial.

(vi) r^{2 }

∵ The degree of r^{2} is 2.

∴ It is a quadratic polynomial.

(vii) 7x^{3}

∵ The degree of 7x^{3 }is 3.

∴ It is a cubic polynomial.

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